Range, quartiles , absolute deviation, and variance are all examples of measures of variability. Consider the following data set: 5, 19, 24, 62, 91, The range of that data set is 95, which is calculated by subtracting the lowest number 5 in the data set from the highest Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable's mean, standard deviation, or frequency.
Inferential statistics can help us understand the collective properties of the elements of a data sample. Knowing the sample mean, variance, and distribution of a variable can help us understand the world around us.
These are two commonly employed descriptive statistics. Mean is the average level observed in some piece of data, while standard deviation describes the variance, or how dispersed the data observed in that variable is distributed around its mean. While these descriptives help understand data attributes, inferential statistical techniques—a separate branch of statistics—are required to understand how variables interact with one another in a data set.
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I Accept Show Purposes. Your Money. Personal Finance. This page describes graphical and pictorial methods of descriptive statistics and the three most common measures of descriptive statistics central tendency, dispersion, and association. Descriptive statistics can be useful for two purposes: 1 to provide basic information about variables in a dataset and 2 to highlight potential relationships between variables.
The three most common descriptive statistics can be displayed graphically or pictorially and are measures of:. There are several graphical and pictorial methods that enhance researchers' understanding of individual variables and the relationships between variables. Graphical and pictorial methods provide a visual representation of the data. Some of these methods include:.
Each value of a variable is displayed along the bottom of a histogram, and a bar is drawn for each value. Display the relationship between two quantitative or numeric variables by plotting one variable against the value of another variable. For example, one axis of a scatter plot could represent height and the other could represent weight. Each person in the data would receive one data point on the scatter plot that corresponds to his or her height and weight. A GIS is a computer system capable of capturing, storing, analyzing, and displaying geographically referenced information; that is, data identified according to location.
Display networks of relationships among variables, enabling researchers to identify the nature of relationships that would otherwise be too complex to conceptualize. Graphical Analytic Techniques. Geographic Information Systems. Measures of central tendency are the most basic and, often, the most informative description of a population's characteristics. When analysing data, such as the marks achieved by students for a piece of coursework, it is possible to use both descriptive and inferential statistics in your analysis of their marks.
Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results and draw conclusions.
So what are descriptive and inferential statistics? And what are their differences? Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.
Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data. Descriptive statistics are very important because if we simply presented our raw data it would be hard to visualize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables us to present the data in a more meaningful way, which allows simpler interpretation of the data.
For example, if we had the results of pieces of students' coursework, we may be interested in the overall performance of those students. We would also be interested in the distribution or spread of the marks. The statistical measures used in descriptive statistics are the measures of central tendency, measures of spread, and measures of skewness.
A measure of central tendency represents the central point of a dataset which involves the mean, median, and mode. Mean, also called as the average, is simply the sum of the data sets divided by the number of terms. The median, on the other hand, is the value in the middle of a data set while the mode is the number that appears the most in a data set.
If the total number of terms in a data set is an even number, you have to get the two values in the middle and solve for its average to be able to get the median. It is also possible to find more than one mode in a data set which is called multimodal. A measure of spread, also called as the measure of dispersion, describes the variability of the values in a data set.
It involves the computation of range, variance, standard deviation, and quartiles. The range tells the value of the distance between the lowest and the hight value.
Standard deviation is the measure of dispersion in the center of the value, while the variance is the expectation square of the standard deviation. A quartile is classified into three parts: The first quartile or the Q1 is the middle number between the lowest value and the median of the data set. The second quartile Q2 , is the median of the data, while the third quartile Q3 is the middle value between the median and the highest number in the data set.
Skewness is the degree of distribution of a variable about its mean. The value of skewness can either be positive, negative, or undefined.
When the result is zero, it means that no skewness has occurred.
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